Maximin criterion
Max-min criterion for decision making, was presented in writing on year 1950 by Abraham Wald (1902–1950). This criterion represents a pessimistic approach in decision-making (assumes the least favorable situation during taking a decision).
Application
According to the max-min criterion first for each strategy of payoff matrix, we should determine the minimum value. And then choose the strategy, for which the minimum payout, is the largest.
\(v = \underset{i}{max}\{\underset{j}{min}\{a_{ij}\}\}\)
Example
Example: we have an array of payments from the four possible decisions and three possible states:
\( \underset{Strategies}{} \diagdown \overset{States\ of\ nature} {} \) | I | II | III |
T1 | 200 | 100 | 120 |
T2 | 0 | 300 | −200 |
T3 | 0 | 300 | 500 |
T4 | −100 | 200 | 0 |
We are looking for a minimum winnings for each strategy, and then select the largest:
Strategies | \(\underset{j}{min}\{a_{ij}\}\) |
T1 | 100 |
T2 | −200 |
T3 | 0 |
T4 | −100 |
Summing up: According to the Max-min criterion manager should choose a strategy T1.
References
- Hassan, N., Siew, L. W., & Shen, S. Y. (2012). Portfolio decision analysis with maximin criterion in the Malaysian stock market. Applied Mathematical Sciences, 6(110), 5483-5486.